Chapter 10.5, Problem 25E

### Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Chapter
Section

### Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

# Identify the type of conic section whose equation is given and find the vertices and foci.25. 4x2 = y2 + 4

To determine

To Find: The type of conic section, vertices and foci for the equation 4x2=y2+4 .

Explanation

Given:

The equation is as follows.

4x2=y2+4 (1).

Rewrite the equation (1) as below.

4x2âˆ’y2=4

Divide the equation (1) with the value 4 .

4x24âˆ’y24=44

x21âˆ’y24=1 (2).

Then, compare the equation (2) with the standard equation of hyperbola.

x2a2âˆ’y2b2=1

Therefore, the type of conic section is hyperbola.

Calculation:

Compute the center of the hyperbola using the equation:

(xâˆ’h)2a2+(yâˆ’k)2b2=1(xâˆ’0)21âˆ’(yâˆ’0)24=1

Therefore, the center of the hyperbola (h,k) is (0,0) .

Substitute the value 1 for a2 and 4 for b2 in equation (2).

a2=1a=1

b2=4b=4b=2

Compute the vertices

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